The simple gauged \(U(1)\)  extension of the SM is based on the gauge group \(SU(3)_c\otimes SU(2)_L\otimes U(1)_Y\otimes U(1)_X\) .
The particle content of the model is listed in Tab. REF .
We consider a conventional case that the \(U(1)_X\)  charge assignment is flavor-universal [1]}.
In addition to the \(U(1)_X\)  gauge boson \(Z^\prime \) , three RHNs and one \(U(1)_X\)  Higgs field (\(\Phi \) ) are introduced.
The particle content of the model is basically the same as the one of the minimal \(B-L\)  model
while the \(U(1)_X\)  charge of each SM field is generalized to a linear combination of
its \(U(1)_Y\)  and \(B-L\)  charges with real parameters \(x_H\)  and \(x_\Phi \) .
In the presence of three RHNs, this model is anomaly-free.
Since the \(U(1)_X\)  gauge coupling is a free parameter, we can set \(x_\Phi =1\)  without loss of generality.
The minimal \(B-L\)  model is realized in the minimal \(U(1)_X\)  model as the limit of \(x_H \rightarrow 0\) .
